Can EPW calculate self-enegy based on the HSE bandstructure??

[sanders]

Dear EPW users:
Since the hybrid functional HSE can accurately predict the band structure, the electronic properties, such as electron conductivity, Seebeck coefficients, and power factor and be accurately determined based on HSE band structure. Whether the electron self-energy can be calculated based on the HSE band structure using QE+EPW?

[hlee]

Dear sanders:

To calculate the electron self-energy, in addition to energy eigenvalues and wavefunctions, you need electron-phonon matrix elements (which rely on the perturbing potential dvscf), phonon frequencies, etc.

Currently, in QE, DFPT is not compatible with hybrid functional.
Therefore, you can't obtain the perturbing potential and phonon frequencies which are corrected due to hybrid functional; instead, for example, you can just calculate the electron self-energy with energy eigenvalues corrected due to hybrid functional by using the EPW's input flag of eig_read.

(Excerpt from the EPW website)

Code: Select all

Variables:      eig_read

   Type:           LOGICAL
   Default:        .false.
   Description:    If .true. then read a set of eigenvalues from ksdata.fmt
                                 Can be used to read GW (or other) eigenenergies. The code expect a file called "prefix.eig" to be read. 
                                 One need to provide the same number of bands as in the nscf calculations and all k-points. 

Added after the first post:
I think that the method above (using eig_read) doesn't work in case of the change in band ordering in hybrid-functional calculations; so you had better start from the wavefunctions AND energy eigenvalues from hybrid calculations (without using eig_read). However, as I already mentioned, even in this case, the electron-phonon matrix elements and phonon frequencies, etc. (other ingredients of electron self-energy) are not corrected due to hybrid functional.

Sincerely,

H. Lee

[sanders]

Dear Lee:

Is there any example about how to use the input flag of eig_read? If no, could you please show us an example?

Sincerely,

Sanders

[hlee]

Dear sanders:

You can consult the following page for the use of eig_read with the external eigenvalues from Yambo (GW code)
https://github.com/mmdg-oxford/papers/t ... ass_SOC_GW

However, as I mentioned, if you use eig_read in your hybrid-functional case, it just corrects eigenvalues only, and moreover in case of the change in band ordering, it doesn't work.

Sincerely,

H. Lee

[sanders]

Dear Lee:

I have some new questions about your answers above.

(1) You have suggested that I'd better start from the wavefunctions AND energy eigenvalues from hybrid calculations (without using eig_read), but QE didn't support the 'nscf' calculation for hybrid calculations. Did you mean to start with the 'scf' calculation?
(2) By using the input flag 'eig_read', the hybrid-functional only corrects the eigenvalues, and the electron-phonon matrix elements and electron self-energy (or electron linewidths) are the same as the results from PBE functional (Assuming that PBE is used in 'scf' and 'nscf' calculations). Am I right?
(3) If the change in band ordering doesn't appear in the width of the Fermi surface window (controlled by the input flag 'fsthick'), can I use the input flag 'eig_read'?

Sincerely,

Sanders

[hlee]

Dear Sanders:

(1) You have suggested that I'd better start from the wavefunctions AND energy eigenvalues from hybrid calculations (without using eig_read), but QE didn't support the 'nscf' calculation for hybrid calculations. Did you mean to start with the 'scf' calculation?

Yes, I mean the scf calculation. It has some issues since currently EPW needs the information on the full grid, but hybrid calculation generates the information on the irreducible grid; you need unfolding.

(2) By using the input flag 'eig_read', the hybrid-functional only corrects the eigenvalues, and the electron-phonon matrix elements and electron self-energy (or electron linewidths) are the same as the results from PBE functional (Assuming that PBE is used in 'scf' and 'nscf' calculations). Am I right?

You missed one thing; As I said in my first post (see the quote below), the electron self-energy depends on the energy eigenvalues.

To calculate the electron self-energy, in addition to energy eigenvalues and wavefunctions, you need electron-phonon matrix elements (which rely on the perturbing potential dvscf), phonon frequencies, etc.

(3) If the change in band ordering doesn't appear in the width of the Fermi surface window (controlled by the input flag 'fsthick'), can I use the input flag 'eig_read'?

This is too complex to give a clear answer, but my answer is no. I think that there should be no change in band ordering in the band manifold determined by Wannier90, but in general, this is not the case with hybrid calculations.

Sincerely,

H. Lee

[sanders]

Dear Lee:

The last question:

In the HSE scf calculation, if I use the script ''kmesh.pl'' to generate full k-point grids, EPW would work. Is it right?

Sincerely,

Sanders

[hlee]

Dear Sanders:

I didn't check it, but the most important point is that the list and the number of k points in the output of hybrid calculations (See the excerpt below) should be the same as those generated by kmesh.pl.

Excerpt from https://gitlab.com/QEF/q-e/-/blob/devel ... e-si444.in .

Code: Select all

   Cartesian axes

     site n.     atom                  positions (alat units)
         1           Si  tau(   1) = (   0.0000000   0.0000000   0.0000000  )
         2           Si  tau(   2) = (   0.2500000   0.2500000   0.2500000  )

     number of k points=    10
                       cart. coord. in units 2pi/alat
        k(    1) = (  -0.1250000   0.1250000   0.1250000), wk =   0.0625000
        k(    2) = (  -0.3750000   0.3750000  -0.1250000), wk =   0.1875000
        k(    3) = (   0.3750000  -0.3750000   0.6250000), wk =   0.1875000
        k(    4) = (   0.1250000  -0.1250000   0.3750000), wk =   0.1875000
        k(    5) = (  -0.1250000   0.6250000   0.1250000), wk =   0.1875000
        k(    6) = (   0.6250000  -0.1250000   0.8750000), wk =   0.3750000
        k(    7) = (   0.3750000   0.1250000   0.6250000), wk =   0.3750000
        k(    8) = (  -0.1250000  -0.8750000   0.1250000), wk =   0.1875000
        k(    9) = (  -0.3750000   0.3750000   0.3750000), wk =   0.0625000
        k(   10) = (   0.3750000  -0.3750000   1.1250000), wk =   0.1875000

As I already mentioned several times, even in this case, these corrections are partial and there are several inconsistencies; for example, in the evaluation of electron-phonon matrix elements, the wave functions come from hybrid calculations, but the perturbing potential from normal DFT calculations.

It is up to you to decide whether it makes sense.

Sincerely,

H. Lee